Ammann, Bernd and Mougel, Jeremy and Nistor, Victor (2022) A Comparison of the Georgescu and Vasy Spaces Associated to the N-Body Problems and Applications. ANNALES HENRI POINCARE, 23 (4). pp. 1141-1203. ISSN 1424-0637, 1424-0661
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We provide new insight into the analysis of N-body problems by studying a compactification M-N of R-3N that is compatible with the analytic properties of the N-body Hamiltonian H-N. We show that our compactification coincides with a compactification introduced by Vasy using blow-ups in order to study the scattering theory of N-body Hamiltonians and with a compactification introduced by Georgescu using C*-algebras. In particular, the compactifications introduced by Georgescu and by Vasy coincide (up to a homeomorphism that is the identity on R-3N). Our result has applications to the spectral theory of N-body problems and to some related approximation properties. For instance, results about the essential spectrum, the resolvents, and the scattering matrices of H-N (when they exist) may be related to the behavior near M-N\R-3N (i.e., "at infinity") of their distribution kernels, which can be efficiently studied using our methods. The compactification M-N is compatible with the action of the permutation group S-N, which allows to implement bosonic and fermionic (anti-)symmetry relations. We also indicate how our results lead to a regularity result for the eigenfunctions of H-N.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | INVERSE-SQUARE POTENTIALS; C-ASTERISK-ALGEBRAS; ESSENTIAL SPECTRUM; PSEUDODIFFERENTIAL-OPERATORS; SCHRODINGER-OPERATORS; PERTURBATION-THEORY; FREDHOLM CONDITIONS; MANIFOLDS; HAMILTONIANS; COMPACTIFICATION |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Bernd Ammann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 17 Aug 2022 11:25 |
| Last Modified: | 17 Aug 2022 11:25 |
| URI: | https://pred.uni-regensburg.de/id/eprint/46622 |
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